Question

The denominator of a rational number is less than its numerator than 5. If the 5 is added to the numerator, the new number becomes 11 by 6.Find the original number. ​

Answer 1

Question:-

The denominator of a rational number is less than its numerator than 5. If the 5 is added to the numerator, the new number becomes 11 by 6.Find the original number.

To Find:-

• Find the number.

Solution:-

• Let the numerator be x

• Denominator be x - 5

According to the Question:-

$\sf\longrightarrow \: \dfrac { x + 5 } { x - 5 } = \dfrac { 11 } { 6 }$

$\sf\longrightarrow \: 6( x + 5 ) = 11( x - 5 )$

$\sf\longrightarrow \: 6x + 30 = 11x - 55$

$\sf\longrightarrow \: 11x - 6x = 55 + 30$

$\sf\longrightarrow \: 5x = 85$

$\sf\longrightarrow \: x = \cancel\dfrac { 85 } { 5 }$

$\sf\longrightarrow \: x = 17$

Hence ,

• Numerator is x = 17

• Denominator is x - 5 = 12